The tripod mount for the Mirex tilt-shift adapter allows to shift (and tilt) the camera, while the lens remains fixed. The camera can be rotated, but the shift movement is only left-right (or up-down if the tilt-shift adapter is mounted vertically, for example with a L-bracket). Irrespective of the tripod mount, the tilt movement is perpendicular to the shift movement (as described in my first tilt-shift blog post).
The ability to shift the camera while the lens remains fixed is particularly helpful for taking shift panoramas, which is one of the applications I am most interested in. Attaching the adapter to the tripod head, as opposed to the camera, may also provide a better balance and thus render handling much easier, in particular with heavier lenses and/or small cameras. Despite these advantages, the dedicated tilt-shift lenses I know do not have a tripod mount, which makes the described tilt-shift adapter solution rather unique.
I am very happy with both my tilt-shift adapter and with the new tripod mount that I leave permanently attached (I am too lazy to unscrew and fasten the tripod mount each time I want to use the adapter on a tripod). However, if you hardly ever create stitch panoramas you may not need a tripod mount and definitely not want to permanently "enlarge" your tools with this accessory. For me, the tripod mount for my tilt-shift adapter is a worthwhile accessory, which allowed me to take several nice panoramas, some of which I will show you in upcoming posts.